Patients receive veliparib orally (PO) on days 1-3, 8-10, and 15-17 (veliparib is omitted on days 1-3 of course 2) and topotecan hydrochloride intravenously (IV) over 30 minutes on days 2, 9, and 16. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity.